
"""simple docstring"""



from collections import defaultdict
from math import ceil, sqrt


def 			_UpperCamelCase						(    _A = 1_0_0_0_0_0_0       ,   _A = 1_0   )     ->	int:





    """simple docstring"""

    _UpperCAmelCase        = defaultdict(_A   )

    for outer_width in range(3       ,   (t_limit // 4) + 2   ):
        if outer_width * outer_width > t_limit:
            _UpperCAmelCase        = max(
                ceil(sqrt(outer_width * outer_width - t_limit   )   )       ,   1   )
        else:
            _UpperCAmelCase        = 1

        hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

        for hole_width in range(_A       ,   outer_width - 1       ,   2   ):
            count[outer_width * outer_width - hole_width * hole_width] += 1

    return sum(1 for n in count.values() if 1 <= n <= 1_0   )


if __name__ == "__main__":
 print(F"{solution() = }")

"""simple docstring"""



def 			_UpperCamelCase						(    _A   )     ->	int:





    """simple docstring"""

    if not isinstance(_A       ,   _A   ) or number < 0:
        raise ValueError("""Input must be a non-negative integer"""   )

    _UpperCAmelCase        = 0
    while number:
        # This way we arrive at next set bit (next 1) instead of looping
        # through each bit and checking for 1s hence the
        # loop won't run 32 times it will only run the number of `1` times
        number &= number - 1
        count += 1
    return count


if __name__ == "__main__":
 import doctest

 doctest.testmod()